The answer above is NOT correct. (1 point) Suppose a matrix A has columns that s

Question

The answer above is NOT correct. (1 point) Suppose a matrix A has columns that span Rn. Select the best statement. A. Then the equation Ax 0 will have nontrivial solutions only if one column is a multiple of another column. B. Then the equation Ax = 0 must have nontrivial solutions. C. Then the equation Ax - 0 can have nontrivial solutions, but the shape of the matrix will not give us that information. D. Then the equation Ax0 will have nontrivial solutions precisely when it is not square. E. Then the equation Ax - 0 cannot have nontrivial solutions. OF. none of the above

Explanation / Answer

Answer is E

reason:

Since the columns of A span Rn, this implies rank A =no. of unknowns(as number of columns and unknowns is same)=n.

therefore the homogeneous system will have unique solution , that is the trivial solution . x1=x2=......=xn=0.

therefore, there doesnt exist a non trivial solution

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